1. Field of the Invention
The present invention is directed to logging of formation shear in a borehole traversing an earth formation. More particularly, the present invention is directed to logging of formation shear using discrete frequency measurements, as well as to logging in the frequency domain.
2. Background Information
It has long been an objective of the oil industry to obtain formation shear data from a sonic logging tool. See, for example, J. WHITE, THE HULA LOG: A PROPOSED ACOUSTIC TOOL, presented at the Society of Professional Well Log Analysts Conference, 1967. Shear wave data has been found useful in lithology and fluid indentification, porosity determination, measurement of rock elastic and inelastic properties, and as an adjunct to shear seismic data. See, for example, H. LESLIE and F. MONS, SONIC WAVEFORM ANALYSIS: APPLICATIONS, presented at the Society of Professional Well Log Analysts (SPWLA) Annual Logging Symposium, New Orleans, La. June 10-13, 1984.
Traditional sonic borehole logging tools have been used to acquire formation shear data. Such tools employ a monopole transmitter which emits a broad-band sound pulse, and one or more receivers which detect the pulse as it passes.
A number of such sonic logging tools have been widely used, including Schlumberger's BHC* borehole compensated sonic tool, LSS* long-spaced sonic tool, and Array Sonic* digital sonic tool. (The symbol * indicates a mark of Schlumberger.) The waveform from each receiver of such a tool is recorded as a function of time to produce a sonic log in which the time required for a sound wave to traverse a given distance of the formation is plotted versus depth in the borehole. Such tools have not, however, proven entirely satisfactory for acquisition of formation shear data. For example, it is not always possible to obtain formation shear data in "slow" formations (formations having a shear velocity less than the borehole fluid velocity). A review of how shear data is obtained with these tools helps to understand why this is so.
Propagation of the broad-band, monopole sound pulse in a borehole is governed by the mechanical properties of several separate acoustic domains. These include the formation, the borehole fluid column, and the logging tool itself. Wide-band sound energy emanating from the monopole transmitter impinges on the borehole wall, establishing compressional and shear waves in the formation, surface waves along the borehole wall, and guided waves within the fluid column. The borehole wall, formation bedding, borehole rugosity, and fractures can all represent significant acoustic discontinuities. The phenomena of wave refraction, reflection and conversion lead to the presence of many acoustic waves in the borehole when a sonic log is being run. Thus, many acoustic energy arrivals are seen by the receivers of a sonic logging tool.
The more usual acoustic energy arrivals at the receivers of a sonic logging tool having a wide-band monopole energy source are shown in the waveform examples of FIG. 1. The distinct changes corresponding to the onset of the compressional and shear arrivals and the tube (Stoneley) arrival can be seen in these examples, although the wave packets are not totally separated in time. The first arrival (the compressional wave) has traveled from the transmitter to the formation as a fluid pressure wave, has been refracted at the borehole wall, has traveled within the formation at the compressional wave velocity of the formation, and has traveled back to the receiver as a fluid pressure wave. The shear wave has traveled from the transmitter to the formation as a fluid pressure wave, has traveled within the formation at the shear wave velocity of the formation, and has traveled back to the receiver as a fluid pressure wave. The mud wave (not strongly evident in the wavetrain examples of FIG. 1) has traveled directly from transmitter to receiver in the mud column at the compressional wave velocity of the borehole fluid. The Stoneley wave is of large amplitude and has traveled from transmitter to receiver with a velocity less than that of the compressional waves in the borehole fluid.
Various waveform processing techniques have been used to find and analyze some or all of the propagating waves in composite time-domain waveforms such as those shown in FIG. 1. For example, the slowness-time coherence technique (STC) uses a semblance algorithm to detect arrivals that are coherent across the array of receiver waveforms and to estimate their interval transit time. Applying this semblance algorithm to the waveforms of FIG. 1 produces the coherence map of FIG. 2, in which regions of large coherence correspond to the compressional, shear, and Stoneley arrivals. The apex of each region defines the slowness of that wave. This process is repeated for each set of waveforms acquired by the tool and is used to produce a log of slowness versus depth such as shown in FIG. 3. In a slow formation (a formation having a shear velocity less than the borehole fluid velocity), the tool obtains real-time measurements of compressional, Stoneley and mud wave velocities, but shear wave values must be derived from these velocities.
Despite the progress made in obtaining formation shear data with the traditional monopole, time-domain logging tools, a number of difficulties remain. For example, it has often been found that the amplitude of the shear wave is insufficient for effective processing and analysis. And because the first shear wave arrival follows the compressional wave arrival, identifying the first shear arrival can be difficult or impossible.
Accordingly, various sonic tools have been proposed for directly logging formation shear, particularly in slow formations where the conventional tools having a monopole source cannot give shear wave logs directly. These tools employ dipole or other multipole (e.g., quadrupole) source and receiver transducers (rather than monopole transducers as in conventional sonic logging tools) for direct logging of shear in both fast and slow formations.
A monopole source excites azimuthally symmetric acoustic waves around the borehole, as shown diagrammatically in FIGS. 4a and 4b. As a monopole wave propagates along the hole, the wave causes the borehole cross-section to bulge and contract symmetrically. In contrast, a dipole source can be synthesized from two monopole sources of opposite polarity (i.e., the pressure of one source is positive when the other is negative and vice versa) placed on a plane perpendicular to the borehole axis. Since one side of a dipole source pushes the fluid with a positive pressure and the other side pulls with a negative pressure, a dipole source acts as a point force moving the fluid transversely to the borehole wall. Therefore, propagation of a dipole wave causes the formation surrounding the borehole to flex sideways, as shown diagrammatically in FIGS. 5a and 5b.
A dipole source must move the borehole fluid to vibrate perpendicularly to the borehole axis. This can be achieved by moving a plate in the hole. One way to move the plate is to use the concept of moving coils in a magnetic field, similar to loudspeakers. Another way is to use piezoelectric bimorphic or monomorphic benders. A bimorphic bender is made of two thin piezoelectric plates of opposite polarity bonded together. As a voltage is applied across the plates, one plate extends while the other contracts. Thus, the composite plate bends in response to applied voltage much as a bimetallic plate does in response to temperature change. When supported at the edges, the bender will move the fluid sideways as a dipole source. Other dipole source configurations are also known, such as dual volume sources, expanding rods, rare earth transducers, split cylinders, etc.
A dipole receiver must be able to sense either pressure gradient, particle acceleration, particle velocity, or particle displacement. Measuring the differential output of two hydrophones will give the pressure gradient. Accelerometers and geophones will sense particle acceleration and velocity, respectively. Variable capacitance microphones can sense the displacement of the fluid particle vibrations. These transducers vary in their sensitivities and frequency characteristics.
In contrast to the dipole transducers, which excite and detect pressure gradient or particle vibrations, a quadrupole transducer can excite and detect waves with 90-degree asymmetry. That is, as a quadrupole wave travels up the borehole, the borehole vibration will be like squeezing a paper cup in one direction. In the cross-sectional plane, the wall will squeeze in toward the axis in one direction and expand out away from the axis in the perpendicular direction. Thus, quadrupole transducers will excite and detect shear/screw waves, in contrast to the shear/flexural of dipole transducers.
An early multipole logging tool concept was proposed by J. E. White in 1967. See J. WHITE, THE HULA LOG: A PROPOSED ACOUSTIC TOOL, paper presented at the Society of Professional Well Log Analysts Conference, 1967, and U.S. Pat. No. 3,475,722 to J. E. White. in that proposal, a cluster of piezoelectric transducers is mounted on each of several pads which are pressed against the borehole wall. The transducers of each pad are oriented along mutually orthogonal axes and selectively activated to apply force to the borehole wall in a desired direction. The tool can be operated in one of four different modes to produce torsional, flexural, radial and axial vibrations, by suitable application of voltage pulses to the source transducers. The flexural (sideways) mode of vibration is that of a dipole source.
A subsequent dipole tool concept, which does not require contact with the borehole wall, is disclosed in U.S. Pat. No. 3,593,255 to J. E. White. The transducers in that arrangement are each formed of two half-cylinder segments of piezoelectric material (barium titanate), assembled to form a cylindrical body. The segments are connected electrically such that the application of a voltage causes one segment to expand in the radial direction when the other segment contracts in the radial direction, and vice versa, thereby generating a dipole wave in the borehole. The receiver transducers are of the same construction, acting as a pressure gradient sensor at low frequencies. A voltage pulse is applied to the source transducer to produce a flexural wave in the borehole, and the response of the receiver transducer is displayed in time domain.
A further proposal for low-frequency dipole shear logging is found in C. KITSUNEZAKI, A New Method for Shear-wave Logging, 45 Geophysics 10, at 1489-1506 (October, 1980). In that arrangement, a force applied to a rigid body suspended in the borehole fluid produces pressure changes at front and rear surfaces of the body. The borehole wall is excited indirectly by the fluid pressure changes. The electrodynamic source transducer employs a moving coil and a permanent magnet. As shown in U.S. Pat. No. 4,207,961 to Kitsunezaki, the moving coil drives a diaphragm which displaces the fluid to excite dipole waves in the borehole. The receivers are geophone-like devices with a neutrally-buoyant body which moves relative to the logging tool in response to passage of the asymmetric dipole pressure wave. A pulse is applied to the source transducer, and the waveforms detected at the receivers are recorded in the time domain. The tool must be stationary while taking measurements. An alternate transducer construction proposed in U.S. Pat. No. 4,207,961 to Kitsunezaki has diaphragms which move up and down such that a pair of fluid chambers displace fluid in opposite directions to generate a dipole wave.
A modification of Kitsunezaki's electrodynamic transducer, disclosed in U.S. Pat. No. 4,383,591 to Ogura, generates both monopole and dipole signals. Since the original design by Kitsunezaki was unsuitable for logging shear in fast formations, a new design was developed which uses a stationary coil and a moving magnet or a magnetic material block. The moving magnet is used as a hammer to drive either a rubber or a metal plate. The frequency was extended to several kHz and the power output was increased by the new design. See K. TANAKA, S. INOUE and K. OGURA, DEVELOPMENT OF A SUSPENSION PS LOGGING SYSTEM'S SEISMIC SOURCE FOR HARD GROUND, presented at the 56th SEG Annual Meeting, Houston, Texas, Nov. 2-6, 1986.
In 1984, results of time-domain dipole shear logging using piezoelectric bimorphic bender transducers were published. See J. ZEMANEK, F. ANGONA, D. WILLIAMS and R. CALDWELL, CONTINUOUS ACOUSTIC SHEAR WAVE LOGGING, presented at the 25th SPWLA Logging Symposium, New Orleans, 1984. U.S. Pat. Nos. 4,516,228 to J. Zemanek and 4,649,525 to F. Angona et al. disclose dipole transducers, including both circular and rectangular benders. For the circular bender, the circumference of the bender element is mounted to the sonde by means of a rubber mounting ring. Two edges of the rectangular bender are mounted with rubber mounting strips. The source and receiver transducers are of similar construction. The benders have a resonant frequency such that, when a broad-band voltage pulse is applied to them, the frequency of the resulting acoustic signal ranges from about 1 kHz to 6 kHz with a predominant frequency of about 3 kHz. Benders of lower resonant frequency are also discussed.
Still other multipole logging tools have been proposed. For example, U.S. Pat. No. 4,606,014 to Winbow et al. discloses an acoustic dipole logging device in which the transducers comprise either a bimorphic bender clamped at one edge or a pair of bimorphic benders clamped at opposing edges. The source transducer is driven by a voltage pulse. The outputs of the receiver transducers are band-pass filtered and processed in time domain. U.S. Pat. No. 4,649,526 to Winbow et al. discloses an acoustic logging device with dipole or higher-order multipole transducers having multiple piezoelectric members of split-cylinder or bimorphic plate form. The source transducers are driven by voltage pulses.
U.S. Pat. No. 4,682,308 to Chung and U.K. Patent Application GB 2 158 581 A of Chen et al, filed May 2, 1985, disclose further multipole acoustic logging transducers, including such arrangements as quadrupole transducers having vertically-mounted magnetostrictive rods or piezoelectric stacks, or horizontally mounted magnetostrictive rods or piezoelectric stacks which are attached to vibrating masses.
Several other transducer arrangements have also been proposed, such as an eccentric weight vibrator and clamped geophone to measure shear in the 50 to 300 Hz frequency band (W. BENZING, EXPERIMENTATION IN DOWNHOLE SHEAR WAVE VELOCITY MEASUREMENTS, presented at the SEG Annulal Meeting, Las Vegas, Nevada, Sept. 11-15, 1983), a bender transducer having two stacks of rectangular piezoelectric bars which are pre-stressed in a mounting assembly (G. NUNN and W. CURRIE, BENDER-BAR TRANSDUCERS FOR EARTH ACOUSTIC MEASUREMENTS presentation at the Interwell Seismic Surveying Workshop, Los Alamos, New Mexico, Mar. 24-26, 1988), and a dipole transducer using four rare-earth rods to excite four mass vibrators in the frequency range of 2 kHz to 4 kHz (S. COHIC and J. BUTLER, Rare-earth Iron Square Ring Dipole Transducer, 72 JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA Aug. 2, 1982). U.S. Pat. No. 4,700,803 to Mallett and Minear discloses a magnetostrictive transducer similar to that in the aforementioned U.K. Patent Application GB 2 158 581 A of Chen et al.
However, several difficulties are encountered in obtaining true formation shear from dipole waveforms. First, it has been found that a dipole source excites not only the desired shear waves, but also a borehole flexural wave. A. KURKJIAN and S. CHANG, Acoustic Multipole Sources in Fluid-Filled Boreholes, 51 GEOPHYSICS 1 (January, 1986), at 148-163, and U.S. Pat. Nos. 4,698,792 and 4,703,460 to Kurkjian et al. The flexural wave is dispersive (its phase velocity varies with frequency) and is excited at a greater amplitude than the formation shear by a wide-band dipole source. FIG. 6 illustrates the dispersive nature of the flexural waves as a function of frequency. The flexural wave phase velocity approaches the formation shear velocity at low frequency and gradually becomes slower at higher frequencies. FIG. 7 shows one example of the relative excitation amplitudes of the shear wave and flexural mode as functions of frequency. The direct formation shear is much weaker than the flexural wave at higher frequencies, but stronger than the flexural wave at low frequencies where the flexural wave phase velocity is close to that of the shear velocity. (As shown in the example of FIG. 7, the flexural mode is more than 20 dB stronger than the shear wave above a certain frequency.) At low frequency, the formation shear is excited more than the flexural wave. Therefore, the dipole signals can be viewed approximately as a mixture of shear and flexural wave, with a velocity dispersion following that of the flexural wave. Since the drop in low-frequency amplitude of the shear wave is quite steep, it is difficult to obtain reasonable shear signal strength without also exciting the flexural mode.
Second, to get formation shear, a dipole tool must be operated at very low frequencies where the shear excitation can be very weak.
Third, road noise (the noise generated by the sonde traveling in the borehole) can be very significant at low frequencies. Transverse vibration of the tool is generally detected by the dipole receivers. It has been found that road noise energy is mainly concentrated below 1 kHz and that, in general, road noise increases with increased logging speed.
Finally, the hole conditions in soft rocks can be poor, frequently making the dipole signals very weak in soft rock wells. Of all these difficulties, signal-to-noise ratio and wave dispersion are of primary concern.
As noted above, sonic logging measurements have traditionally been made in time domain: a broad-band sonic energy source excites propagation of sonic waves in the borehole, and waveforms detected at an array of receiver locations spaced from the source in the borehole are recorded as functions of time. Shear wave velocity at the dominant frequency is then estimated by waveform stacking techniques, such as semblance or radon transforms. However, time-domain recording has several disadvantages if the frequency domain results are desired. The waveforms must be sampled in small time steps over a long period, resulting in a large set of data to transmit, store, and process. The truncation in time can cause interference in the processing. In addition, the signal to noise ratio can be quite small for the wide-band transient measurements. The noise problem can be significant for low frequency data (less than 1000 Hz) because of the noises generated by the sonde traveling in the borehole.
In accordance with the present invention, measurements are taken in frequency domain, thereby avoiding the above-noted problems. A frequency domain measurement is desirable for a tool that gives a single dominant arrival. This is particularly true if the arrival is dispersive, as is the case with the shear/flexural arrival of dipole waves.
In contrast to the traditional time-domain logging techniques, U.S. Pat. No. 3,330,375, issued July 11, 1967 to J.E. White proposes a form of acoustic well logging in which the propagation velocities of compressional, shear, mud and casing waves are determined from the expression velocity=frequency.times.wavelength by employing transmitter and/or receiver tuning techniques to determine the wavelength for a known frequency. A variety of such techniques are disclosed, involving wavelength tuning by varying frequency and/or phase shift. In all the techniques, frequency and/or phase shift is adjusted until an amplitude peak is observed, the frequencies which produce such amplitude peaks are noted, and wave propagation velocity is calculated from the expression given above. In one such technique, the wavelength of the transmitted signal is tuned to a fixed wavelength of the transmitting and receiving arrays by varying its frequency. In another, the wavelength of the arrays is tuned to a fixed value of the transmitted wavelength by varying the phase shift between adjacent transducer elements. In another, the frequency of the transmitted signal or the phase shift between adjacent receiving transducers, or both, are varied.
The logging techniques of U.S. Pat. No. 3,330,375 would have a number of disadvantages for shear/flexural or shear/screw wave logging. For example, use of monopole sources significantly reduces the signal-to-noise ratio of the shear/flexural waves, since much of the emitted sonic energy from the monopole source will propagate in compressional rather than shear/flexural mode. Further, the disclosed method and apparatus are directed to determination of wave velocity, and do not provide for logging of amplitude and phase so that both velocity and attenuation can be determined as functions of frequency. Because of the dispersive nature of the shear/flexural mode (wave velocity varies with frequency), both amplitude and phase (or real and imaginary parts) of shear wave energy are needed to understand the dispersion. Furthermore, the disclosed method requires downhole tuning of the frequency and/or the wavelength while acquiring the data. The method is not directly applicable to obtain the frequency dependent characteristics of dispersive waves, such as the shear/flexural or shear/screw waves.
In another approach, U.S. Pat. No. 4,419,748, issued Dec. 6, 1983 to R. W. Siegfried, II., proposes a continuous wave sonic logging method in which a continuous sine wave at a single frequency is emitted and received, and a spatial Fourier transform is performed over the receiver array. The resulting spatial frequency components are then used to indicate the velocities of various sonic paths. The logging method of U.S. Pat. No. 4,419,748 would have several disadvantages for multipole shear logging. For example, the method requires a large number of receivers in order to facilitate the spatial Fourier transforms. Further, the disclosed method records the instantaneous values of the received signal; that is, it is recorded in time domain. Therefore, the measurement is subject to noise interferences. No improvement in the signal to noise ratio is realized by the proposed method. Furthermore, the measurement can only be done one frequency per logging run (due to the time domain recording). This would require numerous logging runs for the dispersive waves, for which the wave characteristics are functions of frequency. Since the logging time is a costly factor in wire line logging services, the method is not practical for logging dispersive waves.
It is an object of the present invention to provide methods and apparatus for borehole shear/flexural logging in which the aforementioned disadvantages of the prior art are avoided.
It is a further object of the present invention to provide methods and apparatus for borehole shear wave logging in which amplitude and phase (or real and imaginary parts) of shear/flexural energy propagated in the borehole and surrounding formation are detected for use in determining parameters such as shear wave phase velocity and shear wave attenuation as functions of frequency.
These and other objects of the present invention will become apparent from the description which follows with reference to the accompanying drawing.